Question

The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2017 an average of three residential properties were auctioned off each weekday in the city of New York, up from an average of one per week in 2011. Use Excel functions to compute the probabilities. Write the Excel function to the solution.

1. What is the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2017 in New York?
2. What is the probability that at least one foreclosure auction occurred in New York on a randomly selected weekday of 2017?
3. What is the probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2017 in New York?
4. What is the probability that exactly 10 foreclosure auctions occurred during a randomly selected five-day week in 2017 in New York?

Answer 1

Result:

The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2017 an average of three residential properties were auctioned off each weekday in the city of New York, up from an average of one per week in 2011. Use Excel functions to compute the probabilities. Write the Excel function to the solution.

What is the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2017 in New York?

Poisson distribution used with mean =3

P( x=4) = 0.1680

Excel function: =POISSON.DIST(4,3,FALSE)

What is the probability that at least one foreclosure auction occurred in New York on a randomly selected weekday of 2017?

P ( x ≥1) = 1-P( x=0)

= 0.9502

Excel function: =1-POISSON.DIST(0,3,FALSE)

What is the probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2017 in New York?

P( x≤2) = P( x=0)+P( x=1)+P( x=2)

=0.0498+0.1494+0.2240

    =0.4232

Excel function: =POISSON.DIST(0,3,FALSE)+ POISSON.DIST(1,3,FALSE)+ POISSON.DIST(2,3,FALSE)

OR

Excel function: =POISSON.DIST(2,3,TRUE)

What is the probability that exactly 10 foreclosure auctions occurred during a randomly selected five-day week in 2017 in New York?

   Mean foreclosure auction occurred per five day week = 5*3= 15

P( x=10) = 0.0486

Excel function: =POISSON.DIST(10,15,FALSE)